Question

The machine gun fires 240 bullets per minute if the mass of each bullet is 10 g and the velocity of the bullet is 600m per s the power (in KW) of the gun is

Answer 1

the answer of your question is 14400

Answer 2

Answer:

The machine gun fires 240 bullets per minute if the mass of each bullet is 10 g and the velocity of the bullet is 600m per s the power (in KW) of the gun is $7.\ KW$

Explanation:

Power of the gun can be simply defined as the rate of work done or the amount of energy converted per unit time. It can be expressed as,

Power (P)  $= \frac{Work\\ done\ (W)}{time\ (t)}$  ...(1)

Work done by the bullet will be equal to the change in kinetic energy which can be written as,

$K.E = \frac{1}{2} m v^{2}$  

where m - The mass of the bullet  and

           v - velocity

Let n be the number of bullets,

then power becomes,

$\text { Power }=n \times \frac{\frac{1}{2} m v^{2}}{t}$

Or

$P= \frac{n}{t} \times \frac{1}{2} m v^{2}$    ...(2)

In the question, it is given that,

$m = 10\ g = 0.01\ kg$

$v= 600\ m/s$

$\frac{n}{t} = \frac{240\ bullets}{minute}$

   $=\frac{ 240}{60\ s} = 4\ bullets\ per\ second$

Substitute the above values into equation(2)

We get,

$P= 4\times \frac{1}{2} \times0.01\times 600^{2}$

    $= 7200\ Watt = 7200\times 10^{-3}\ KW$

    $= 7.2 KW$

   

• The power $7.2\ KW$